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Simplifying 4x2 + 16x = 189 Reorder the terms: 16x + 4x2 = 189 Solving 16x + 4x2 = 189 Solving for variable 'x'. Reorder the terms: -189 + 16x + 4x2 = 189 + -189 Combine like terms: 189 + -189 = 0 -189 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -47.25 + 4x + x2 = 0 Move the constant term to the right: Add '47.25' to each side of the equation. -47.25 + 4x + 47.25 + x2 = 0 + 47.25 Reorder the terms: -47.25 + 47.25 + 4x + x2 = 0 + 47.25 Combine like terms: -47.25 + 47.25 = 0.00 0.00 + 4x + x2 = 0 + 47.25 4x + x2 = 0 + 47.25 Combine like terms: 0 + 47.25 = 47.25 4x + x2 = 47.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 47.25 + 4 Reorder the terms: 4 + 4x + x2 = 47.25 + 4 Combine like terms: 47.25 + 4 = 51.25 4 + 4x + x2 = 51.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 2) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 2 = 7.158910532 Simplifying x + 2 = 7.158910532 Reorder the terms: 2 + x = 7.158910532 Solving 2 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.158910532 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.158910532 + -2 x = 7.158910532 + -2 Combine like terms: 7.158910532 + -2 = 5.158910532 x = 5.158910532 Simplifying x = 5.158910532Subproblem 2
x + 2 = -7.158910532 Simplifying x + 2 = -7.158910532 Reorder the terms: 2 + x = -7.158910532 Solving 2 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.158910532 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.158910532 + -2 x = -7.158910532 + -2 Combine like terms: -7.158910532 + -2 = -9.158910532 x = -9.158910532 Simplifying x = -9.158910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.158910532, -9.158910532}
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